This error occurs when a Battle.net or BNLS server is unreachable. It appears like this:
[BNLS] Error 10060: The attempt to connect timed out [BNLS] The server took too long to respond to your computer. The BNLS server appears to be unreachable at this time.
To solve this problem, select a different BNLS or Battle.net server, or enable the Server Selector.